全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

动力系统双曲对称的高效生成方法

, PP. 76-81

Keywords: 双曲几何,动力系统,同变性映射,颜色方案

Full-Text   Cite this paper   Add to My Lib

Abstract:

对对称模型分形图形自动生成方法的探索一直是动力系统研究的一个重要分支.本文提出了一种利用动力系统方法自动生成丰富的双曲图案的算法.通过构造动力系统群下具有同变性属性的映射方程,将单位圆内的点变换到基本域内,通过动力系统群的映射,由基础域上的图形及其变换,就可得到覆盖整个区域且仅在边界处重叠的图像.根据连续两点间的双曲距离给点附颜色,这种颜色方案不仅反映了通过特定数目迭代后各个轨迹点的收敛速率,而且由于动力系统群的同变性属性,对称点拥有相同的颜色,所以生成的图像具有对称性,增强了生成图案的艺术感染力.使用该方法可以生成一系列双曲模型图案.

References

[1]  Chung K W,Chan H S,Wang B N.Tessellation in three-dimentional hyperbolic space from dynamics and the quaternions[J].Chaos,Solitons and Fractals,2001,12(10):1 941-1 945.
[2]  Adcock B,Jones K C,Reiter C A.Iterated function systems with symmetry in the hyperbolic symmetry[J].Computer and Graphics,2000,24(5):791-796.
[3]  叶瑞松,欧阳培昌.动力系统结合扩张模群自动生成彩色对称图形[J].汕头大学学报:自然科学版,2005,20(4):14-19.
[4]  Ye Ruisong,Ouyang Peichang.Automatic generation of colored symmetric patterns by dynamical systems with the extended modular group[J].Journal of Shantou University:Natural Science Edition,2005,20(4):14-19.(in Chinese)
[5]  Coxeter H S M,Moser W O J.Generators and Relations for Discrete Groups[M].4th ed.New York:Springer,1980.
[6]  Beardon A F.The Geometry of Discrete Groups[M].New York:Springer,1983.
[7]  Trudeau R J.The Non-Euclidean Revolution[M].Boston:Birkhauser,1987.
[8]  Escher M C.Escher on Escher:Exploring the Infinity[M].New York:Harry N Abrams,1989.
[9]  Dunhan D.Hyperbolic symmetry[J].Computers and Mathematics with Applications,1986,12B(1/2):139-153.
[10]  King G,Stewart I.Nonlinear Equations in the Applied Sciences[M].New York:Academic Press,1992:257-315.
[11]  Chung K W,Chan H S.Symmetrical patterns from dynamics[J].Computer Graphics Forum,1993,12(1):33-40.
[12]  Field M,Golubitsky M.Symmetry in Chaos[M].New York:Oxford University Press,1992.
[13]  Brisson G F,Gartz K M,McCune B J.Symmetric attractors in three-dimentional space[J].Chaos,Solitons and Fractals,1996,7(7):1 033-1 051.
[14]  Chung K W,Chan H S,Wang B N.Hyperbolic symmetries from dynamics[J].Computers and Mathematics with Applications,1996,30(2):33-47.
[15]  Chan H S Y,Chung K W,Wang B N.Computer generation of symmetrical patterns from dynamical systems[C]//Proceedings of the International Conference of Chinagraph.Hangzhou,1996(96):497-501.
[16]  Chung K W,Chan H S Y,Wang B N.Tessellation with the modular group from dynamics[J].Computer and Graphics,1997,21(4):523-534.
[17]  Carter K W,Eagles R L,Grimes S M.Chaotic attractors with discrete planar symmetry[J].Chaos,Solitons and Fractals,1998,9(12):2 031-2 054.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133